The $\kappa$-generalised Distribution for Stock Returns

TL;DR

The paper demonstrates that the $ppa$-generalised distribution effectively models heavy-tailed stock returns, fitting historical data for major indices better than traditional models.

Contribution

It introduces the $ppa$-generalised distribution as a new candidate for modeling stock returns and validates its effectiveness with empirical data.

Findings

The $ppa$-distribution fits a significant portion of stock return data.

Monte Carlo tests support its suitability for financial return modeling.

It outperforms some traditional distributions in capturing heavy tails.

Abstract

Empirical evidence shows stock returns are often heavy-tailed rather than normally distributed. The $\kappa$-generalised distribution, originated in the context of statistical physics by Kaniadakis, is characterised by the $\kappa$-exponential function that is asymptotically exponential for small values and asymptotically power law for large values. This proves to be a useful property and makes it a good candidate distribution for many types of quantities. In this paper we focus on fitting historic daily stock returns for the FTSE 100 and the top 100 Nasdaq stocks. Using a Monte-Carlo goodness of fit test there is evidence that the $\kappa$-generalised distribution is a good fit for a significant proportion of the 200 stock returns analysed.